Weirder things have happened. But if you try to do it without a lawyer, you'll be laughed out of court.
Have you got a competent lawyer representing you in the suit against you? If the photos clearly show no damage, they should be able to stop the suit in its tracks.
You wouldn't be able to sue them under your car insurance. That covers only your liability to other people, not their liability to you. The insurance has nothing to do with that.
It would be a matter of a personal lawsuit having nothing to do with cars, but after the fact... a lawyer would be able to advise you how to go about it, if at all possible. It would likely involve something like going and getting a psych evaluation, going to the trauma ward, or going to court on your current case wearing a neck brace.
That is the big wild card in accident cases, of course. Back and spinal injuries. Because it's medially recognized that you can suffer trauma even though they can't detect it through tests, it is very difficult to disprove that you have an injury. If you prove it was the other guy's fault, then you've got them on the hook for an injury. It's an old trick but it's risky too, if they ever prove you made it up. This forum thread would be evidence of that so you probably shouldn't try the fake back injury trick.
Your lawyer might hate me for even mentioning it.
Since you believe in Karma, you might be interested to hear that Karma never affects you during the same lifetime. It's not the same as "what goes around, comes around" or "tit for tat." It's whatever you did in a past life coming back to you in this one, and often in completely different form.